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FAST gradient algorithm WITH DRY-LIKE FRICTION AND NONMONOTONE LINE SEARCH FOR NONCONVEX OPTIMIZATION PROBLEMS

SIAM JOURNAL ON OPTIMIZATION 2024年第3期34卷 2557-2587页

作者： Nguyen, Lien t. Eberhard, Andrew Yu, Xinghuo Li, Chaojie RMIT Univ Sch Sci Melbourne Vic 3000 Australia RMIT Univ Sch Engn Melbourne Vic 3000 Australia Univ New South Wales Sch Elect Engn & Telecommun Kensington NSW 2033 Australia

In this paper, we propose a fast gradient algorithm for the problem of minimizing a differentiable (possibly nonconvex) function in Hilbert spaces. We first extend the dry friction property for convex functions to what we call the dry-like friction property in a nonconvex setting, and then employ a line search technique to adaptively update parameters at each iteration. Depending on the choice of parameters, the proposed algorithm exhibits subsequential convergence to a critical point or full sequential convergence to an ``approximate"" critical point of the objective function. We also establish the full sequential convergence to a critical point under the Kurdyka--\Lojasiewicz (KL) property of a merit function. Thanks to the parameters' flexibility, our algorithm can reduce to a number of existing inertial gradient algorithms with Hessian damping and dry friction. By exploiting variational properties of the Moreau envelope, the proposed algorithm is adapted to address weakly convex nonsmooth optimization problems. In particular, we extend the result on KL exponent for the Moreau envelope of a convex KL function to a broad class of KL functions that are not necessarily convex nor continuous. Simulation results illustrate the efficiency of our algorithm and demonstrate the potential advantages of combining dry-like friction with extrapolation and line search techniques.

关键词： gradient algorithm dry friction inertial techniques KL property line search linear convergence Moreau envelope nonconvex optimization proximal operator

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A fixed-time gradient algorithm for distributed optimization with inequality constraints

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NEUROCOMPUTING 2023年 532卷 106-113页

作者： He, Xing Wei, Boyu Wang, Hui Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China Chongqing Normal Univ Sch Math Sci Chongqing 401331 Peoples R China

In this paper, a distributed fixed time gradient algorithm for neurodynamic systems is proposed for solv-ing optimization problems with local inequality constraints. The algorithm is designed using fixed time theory and sliding model control techniques, where each agent has a local objective function known only to itself, and the optimal solution of each local objective function sum can be obtained in a fixed time by the information interaction between neighbors under the condition of local inequality constraints. In addition, the upper bound of the fixed time can be obtained and it is proved theoretically that the upper bound of the fixed time is independent of the initial value. Finally, the stability and effectiveness of the algorithm are verified by numerical examples.(c) 2023 Elsevier B.V. All rights reserved.

关键词： gradient algorithm Fixed time convergence Distributed optimization Load sharing control

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Deconvolution beamforming based on a fast gradient algorithm for sound source localization

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JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL 2023年第2期42卷 703-718页

作者： Zan, Ming Xu, Zhongming Zhang, Zhifei Tang, Zhonghua Huang, Linsen Chongqing Univ Coll Mech & Vehicle Engn 74 Shazheng St Chongqing 400030 Peoples R China

Deconvolution beamforming has gotten increased attention as a way to improve the spatial resolution of delay-and-sum beamforming. It has the ability to decrease sidelobes and increase resolution. However, compared to conventional beamforming, the extra computation of the deconvolution method is a drawback. A more efficient approach is developed to improve the computing speed of the deconvolution method. Specifically, when tackling deconvolution problems, this method improves computational performance by combining Fourier operation with a fast gradient algorithm called the double momentum gradient algorithm. We compare the proposed method with two known effective deconvolution methods, namely the fast Fourier transform non-negative least squares algorithm and the fast iterative shrinkage threshold algorithm. The results of simulation and experiment reveal that the proposed method tends to give a better spatial resolution within a short computational time and is more suitable for engineering applications.

关键词： sound localization beamforming deconvolution Fourier gradient algorithm

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An accelerated proximal gradient algorithm for source-independent waveform inversion

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JOURNAL OF APPLIED GEOPHYSICS 2020年 177卷 104030-104030页

作者： Fu, Hongsun Ma, Mingyue Han, Bo Dalian Maritime Univ Sch Sci Dalian 116026 Peoples R China Harbin Inst Technol Dept Math Harbin 150001 Peoples R China

Full Waveform Inversion (FWI) is a promising method for reconstructing subsurface parameters from the full information content in the seismogram. However, FWI is facing many difficulties in practice. The lack of the source wavelet information, the nonlinearity of the forward problems, and ill-posedness of the formulation all contribute to a pressing need for novel regularization techniques and fast algorithms to speed up and improve inversion results. In this paper, by making use of the variable projection method for nonlinear least squares problems, we develop a source-independent frequency-domain FWI strategy. Specifically, the source wavelet for each frequency is removed automatically using a minimum norm solution between the measured and simulated data. Therefore, the inversion process becomes source independent. In order to overcome the defects of overly smoothed edges caused by the classical Tikhonov regularization, sparsity constrained regularization is applied to FWI based on the ability of curvelets to efficiently represent geophysical images. However, non-differentiability of the objective function make it challenging to find an efficient numerical solution. By using the proximal mapping and the Barzilai-Borwein step size rule, we derive a new accelerated proximal gradient algorithm to handle such non-smooth objective functions. The numerical examples show that very good reconstruction results can be obtained by the proposed algorithm without knowledge of the source. Compared to the gradient descent method with a constant step size, the accelerated algorithm gaves a superior result with much higher resolution. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Full waveform inversion Sparsity constrained regularization Variable projection method Proximal operator gradient algorithm

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A gradient algorithm for the identification of interconnected discrete time varying systems

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ENGINEERING COMPUTATIONS 2020年第3期37卷 909-928页

作者： Ghoul, Yamna Tunis El Manar Univ Natl Engn Sch Tunis Concept & Control Syst Beja Tunisia

Purpose An identification scheme to identify interconnected discrete-time (DT) varying systems. Design/methodology/approach The purpose of this paper is the identification of interconnected discrete time varying systems. The proposed technique permits the division of global system to many subsystems by building a vector observation of each subsystem and then using the gradient method to identify the time-varying parameters of each subsystem. The convergence of the presented algorithm is proven under a given condition. Findings The effectiveness of the proposed technique is then shown with application to a simulation example. Originality/value In the past decade, there has been a renewed interest in interconnected systems that are multidimensional and composed of similar subsystems, which interact with their closest neighbors. In this context, the concept of parametric identification of interconnected systems becomes relevant, as it considers the estimation problem of such systems. Therefore, the identification of interconnected systems is a challenging problem in which it is crucial to exploit the available knowledge about the interconnection structure. For time-varying systems, the identification problem is much more difficult. To cope with this issue, this paper addresses the identification of DT dynamical models, composed by the interconnection of time-varying systems.

关键词： Convergence Discrete-time systems gradient algorithm Interconnected systems Time-varying parameters

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Processing parameters optimization algorithm design and verification of suppress subsurface damage based on gradient algorithm

Processing parameters optimization algorithm design and veri...

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Applied Optics and Photonics China (AOPC) Conference - Optics Ultra Precision Manufacturing and Testing

作者： Lin Donglong Yang Baoxi Huang Huijie Xing Yan Zhang Chiliang Chinese Acad Sci Shanghai Inst Opt & Fine Mech Shanghai 201800 Peoples R China Univ Chinese Acad Sci Ctr Mat Sci & Optoelect Engn Beijing 100049 Peoples R China Changchun Natl Extreme Precis Opt Co Ltd Shanghai Branch Shanghai 201800 Peoples R China

ISBN: (纸本)9781510639584

Subsurface damage (SSD) of fused silica elements formed by grinding and polishing will produce high-energy laser modulation and absorption effects. Further induced macro damage will seriously decrease the precision of the optical system and shorten the service life of the optical element. Because of the limit of the optical manufacturing technology, cost, and other reasons, it is hard to grinding and polishing without generating SSD. Thus, efficiently suppress the depth of SSD becomes an important research direction to further enhance the accuracy of the optical system. We use the equations for median and lateral cracks depths to predict the depth of SSD and surface roughness (P -V value). The equations are derived by Lambropoulos from micro indentation mechanics and hill model for indentation of a sharp indenter. The lateral cracks theory and the measurement data on the high-precision roughness measuring instrument are used to solving and verify the grinding empirical formula. This can effectively solve the problems of detecting indentation normal load during process. The empirical formula is then combined with the equations for median and lateral cracks depths to establish an optimization model. With this model, we design an optimization algorithm to optimize the parameters of process to suppress the depth of SSD. gradient algorithm is used to optimize the parameters of the whole process, and design a high efficiency fused silica process solution to obtain a minimal depth of SSD and high-precision surface. The above algorithm has certain universality for different processing machines, materials, and processing conditions. Change the material parameters and constraints can quickly obtain the corresponding processing parameters.

关键词： Subsurface damage Surface roughness gradient algorithm Fused silica

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Thermo-Economic Optimization of Spiral Plate HX by Means of gradient and gradient-Free algorithm

Thermo-Economic Optimization of Spiral Plate HX by Means of ...

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International Conference on Advancement in Materials, Manufacturing and Energy Engineering (ICAMME)

作者： Krishna, Musunuru Hari Dasore, Abhishek Rajak, Upendra Konijeti, Ramakrishna Verma, Tikendra Nath SRK Inst Technol Dept Mech Engn Vijayawada 521108 India RGM Coll Engn & Technol Sch Mech Engn Nandyal 518501 India Koneru Lakshmaiah Educ Fdn Dept Mech Engn Guntur 522502 Andhra Pradesh India Maulana Azad Natl Inst Technol Dept Mech Engn Bhopal 462003 India

ISBN: (纸本)9789811683411;9789811683404

Spiral plate heat exchangers (SPHX) play prominent role in process industries with the fact that rotational motion of the fluid in the channel eliminates the occurrence of fouling. In the present study, thermo-economic optimization of SPHX was performed considering the standard Hall equation as the objective function. For a specified heat duty design, parameters, namely pressure drop in hot and cold fluids, outer spiral diameter, plate length and plate width, are optimized with the objective of minimized cost, using gradient (fmincon) and gradient-free (genetic algorithm (GA)) optimization algorithms. The outcomes were compared to the data attained from experimental works found in the literature. It was found that GA outperforms fmincon in terms of cost minimization. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022.

关键词： gradient algorithm gradient-free algorithm Maximization Spiral plate heat exchanger Thermo-economics

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Adaptive gradient Search algorithm for Displaced Subarrays With Large Element Spacing

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2021年第7期20卷 1155-1159页

作者： Yang, Gongqing Zeng, Hui Xu, Zhenhai Natl Univ Def Technol State Key Lab Complex Elect Environm Effects Elec Informat Syst Changsha 410073 Peoples R China

In this letter, an adaptive gradient search algorithm for displaced subarray optimization is presented. The displaced subarray technique, which is able to suppress the high grating lobes caused by large interelement spacing (i.e., over one-half wavelength), has attracted much attention. In this case, it could reduce the number of active elements as well as the cost of conventional phased array antennas. However, the optimal solution of each displaced subarray location is hard to achieve. The proposed algorithm is a practical method to solve such a nonconvex problem. By gradually reducing the iteration step size, when the search times of each step are enough, the solution is able to converge to a satisfying solution. The effectiveness and the stable performance of our proposed method are verified by various numerical examples.

关键词： Optimized production technology Apertures Gratings Antenna radiation patterns Phased arrays Upper bound Shape Aperture efficiency displaced subarrays gradient algorithm grating lobe (GL) suppression

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Identification of Added Mass and Added Damping Coefficient for an Underwater Shaking Table Based on gradient algorithm 31

Identification of Added Mass and Added Damping Coefficient f...

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31st Chinese Control And Decision Conference (CCDC)

作者： Yao, Jianjun Zhao, Yue Sheng, Tang Qian, Chen Mai, Wangeng Harbin Engn Univ Harbin 150001 Peoples R China

ISBN: (纸本)9781728101057

The underwater shaking table, the key experimental facility for underwater vibration simulation, is used to test the underwater seismic behaviors and vibration characteristics of the underwater equipment such as underwater civil engineering structures and the submarine production system. However, unlike the normal electro-hydraulic servo shaking table, the special working environment of the underwater shaking table brings many difficulties to its design. One of the key issues is that the added mass and the added damping coefficient caused by the fluid-solid coupling problem between the shaking table and the fluid should be considered. These will reduce the bandwidth of the system and low er the system stability to a great extent. In this paper, the FLUENT software and the dynamic meshing technology are applied to establish the finite element model of the underwater shaking table and its fluid domain. Finally, the added mass and the added damping coefficient of the underwater shaking table are identified by using the gradient algorithm. The simulation results show that both the added mass and the added damping coefficient are precisely identified.

关键词： Underwater Shaking Table Added Mass Identification Added Damping Coefficient Identification gradient algorithm Fluid-Solid Coupling

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Fast gradient descent algorithm for image classification with neural networks

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SIGNAL IMAGE AND VIDEO PROCESSING 2020年第8期14卷 1565-1572页

作者： El Mouatasim, Abdelkrim Ibn Zohr Univ FPO BP 284 Ouarzazate 45800 Morocco

Any optimization of gradient descent methods involves selecting a learning rate. Tuning the learning rate can quickly become repetitive with deeper models of image classification, does not necessarily lead to optimal convergence. We proposed in this paper, a modification of the gradient descent algorithm in which the Nestrove step is added, and the learning rate is update in each epoch. Instead, we learn learning rate itself, either by Armijo rule, or by control step. Our algorithm called fast gradient descent (FGD) for solving image classification with neural networks problems, the quadratic convergence rate o(k(2)) of FGD algorithm are proved. FGD algorithm are applicate to a MNIST dataset. The numerical experiment, show that our approach FGD algorithm is faster than gradient descent algorithms.

关键词： gradient algorithm Nesterov algorithm Learning rate control Image classification Neural networks

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